A total of 37 dose-response experiments with essential amino acids performed with rainbow trout and broiler chicken were re-evaluated with different mathematical approaches: an exponential model, a four-parameter logistic function, the saturation kinetics model and the broken line approach. The different approaches were compared both with regard to the goodness of fit (r2 and sy.x) and with regard to the allowances which were derived regarding the optimal amino acid level in the diet. The experimental design, particularly the chosen range in dietary amino acid concentration was found to be important for the comparison of models. Amongst the non-linear models, the four-parameter logistic function and the saturation kinetics model appeared superior to the exponential approach, when the range in dietary amino acid concentration was very wide and included both a severely deficient basal level and a level that exceeded the needs of the animal by approximately the factor 2. In these cases, allowances derived from individual experiments were considerably different depending on the model. The allowances based on the exponential and the saturation kinetics approach were 27.7 and 20.7 g lysine/kg DM and 8.0 and 6.3 g methionine/kg DM, respectively, for rainbow trout. For other amino acids studied in rainbow trout the difference due to model was less. Consequently, the predicted 'ideal protein' for rainbow trout was considerably different depending on the model used. The maximum deviation found in different experiments with broiler chicken for the exponential vs. the saturation kinetics approach was 13.0 and 9.7 g lysine/kg and 11.4 and 8.2 g sulfur-containing amino acids/kg, respectively. However, the more restricted the range in dietary concentration was, the lesser became the differences between the different non-linear models. No definite recommendation can therefore be extracted regarding the most suitable, generally applicable mathematical model.